Question: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 8x + 8$ and $ BC = 5x + 35$ Find $AC$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {8x + 8} = {5x + 35}$ Solve for $x$ $ 3x = 27$ $ x = 9$ Substitute $9$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 8({9}) + 8$ $ BC = 5({9}) + 35$ $ AB = 72 + 8$ $ BC = 45 + 35$ $ AB = 80$ $ BC = 80$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {80} + {80}$ $ AC = 160$